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Previous year question hub

Matrices And Determinants - Algebra - Mathematics Previous Year Questions

Practice Matrices And Determinants - Algebra - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

16Papers
15Years
74Questions
1Topics

Matrices And Determinants question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Matrices And Determinants. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 74 100%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 73 98.6%
Subjective 1 1.4%

Subject weightage

Top subjects by unique question coverage.

Mathematics
74 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
74 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Matrices And Determinants
74 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

WB JEE 2025
8 Qs
VITEEE 2025
1 Qs
WB JEE 2024
6 Qs
WB JEE 2023
5 Qs
WB JEE 2022
6 Qs
WB JEE 2021
7 Qs
WB JEE 2020
6 Qs
WB JEE 2019
6 Qs
WB JEE 2018
6 Qs
WB JEE 2017
6 Qs
WB JEE 2016
2 Qs
WB JEE 2012
1 Qs
WB JEE 2011
5 Qs
WB JEE 2010
4 Qs
WB JEE 2009
3 Qs
WB JEE 2008
2 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
VITEEE 202520251View paper
WB JEE 202520258View paper
WB JEE 202420246View paper
WB JEE 202320235View paper
WB JEE 202220226View paper
WB JEE 202120217View paper
WB JEE 202020206View paper
WB JEE 201920196View paper
WB JEE 201820186View paper
WB JEE 201720176View paper
WB JEE 201620162View paper
WB JEE 201220121View paper
WB JEE 201120115View paper
WB JEE 201020104View paper
WB JEE 200920093View paper
WB JEE 200820082View paper

All Matrices And Determinants previous year questions

Practice every matching question in batches of 20, with every available option.

1
2016 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2016
Let A be a 3 \(\times\) 3 matrix and B be its adjoint matrix. If | B | = 64, then | A | is equal to
A
\(\pm\)2
B
\(\pm\)4
C
\(\pm\)8
D
\(\pm\)12
Open complete paper
2
2016 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2016
If x, y and z are greater than 1, then the value of \(\left| {\matrix{ 1 & {{{\log }_x}y} & {{{\log }_x}z} \cr {{{\log }_y}x} & 1 & {{{\log }_y}z} \cr {{{\log }_z}x} & {{{\log }_z}y} & 1 \cr } } \right|\) is
A
log x . log y . log z
B
log x + log y + log z
C
0
D
1 \(-\) {(log x) . (log y) . (log z)}
Open complete paper
3
2017 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2017
The value of det A, where \(A\, = \left( {\matrix{ 1 & {\cos \theta } & 0 \cr \[{ - \cos \theta } & 1 & {\cos \theta } \cr\] \[{ - 1} & { - \cos \theta } & 1 \cr\] } } \right)\), lies
A
in the closed interval [1, 2]
B
in the closed interval [0, 1]
C
in the open interval (0, 1)
D
in the open interval (1, 2)
Open complete paper
4
2017 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2017
The linear system of equations

\(\left. \matrix{ 8x - 3y - 5z = 0 \hfill \cr 5x - 8y + 3z = 0 \hfill \cr 3x + 5y - 8z = 0 \hfill \cr} \right\}\) has
A
only zero solution
B
only finite number of non-zero solutions
C
no non-zero solution
D
infinitely many non-zero solutions.
Open complete paper
5
2017 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2017
Let P be the set of all non-singular matrices of order 3 over R and Q be the set of all orthogonal matrices of order 3 over R. Then,
A
P is proper subset of Q
B
Q is proper subset of P
C
Neither P is proper subset of Q nor Q is proper subset of P
D
P \(\cap\) Q = \(\phi\), the void set
Open complete paper
6
2017 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2017
Let \(A = \left( {\matrix{ 1 & 1 & 1 \cr 0 & 1 & 1 \cr 0 & 0 & 1 \cr } } \right)\). Then, for positive integer n, An is
A
\(\left( {\matrix{ 1 & n & {{n^2}} \cr 0 & {{n^2}} & n \cr 0 & 0 & n \cr } } \right)\)
B
\(\left( {\matrix{ 1 & 1 & {n\left( {{{n + 1} \over 2}} \right)} \cr 0 & 1 & n \cr 0 & 0 & 1 \cr } } \right)\)
C
\(\left( {\matrix{ 1 & {{n^2}} & n \cr 0 & n & {{n^2}} \cr 0 & 0 & {{n^2}} \cr } } \right)\)
D
\(\left( {\matrix{ 1 & n & {2n - 1} \cr 0 & {{{n + 1} \over 2}} & {{n^2}} \cr 0 & 0 & {{{n + 1} \over 2}} \cr } } \right)\)
Open complete paper
7
2017 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2017
Let a, b, c be such that b(a + c) \(\ne\) 0. If \(\left| {\matrix{ a & {a + 1} & {a - 1} \cr { - b} & {b + 1} & {b - 1} \cr c & {c - 1} & {c + 1} \cr } } \right| + \left| {\matrix{ {a + 1} & {b + 1} & {c - 1} \cr {a - 1} & {b - 1} & {c + 1} \cr {{{( - 1)}^{n + 2}}a} & {{{( - 1)}^{n + 1}}b} & {{{( - 1)}^n}c} \cr } } \right| = 0\), then the value of n is
A
any integer
B
zero
C
any even integer
D
any odd integer
Open complete paper
8
2017 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2017
Let \(A = \left( {\matrix{ {x + 2} & {3x} \cr 3 & {x + 2} \cr } } \right),\,B = \left( {\matrix{ x & 0 \cr 5 & {x + 2} \cr } } \right)\). Then all solutions of the equation det (AB) = 0 is
A
1, \(-\)1, 0, 2
B
1, 4, 0, \(-\)2
C
1, \(-\)1, 4, 3
D
\(-\)1, 4, 0, 3
Open complete paper
9
2018 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2018
The least positive integer n such that \({\left( {\matrix{ \[{\cos \pi /4} & {\sin \pi /4} \cr\] \[{ - \sin {\pi \over 4}} & {\cos {\pi \over 4}} \cr\] } } \right)^n}\) is an identity matrix of order 2 is
A
4
B
8
C
12
D
16
Open complete paper
10
2018 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2018
If \(\left| {\matrix{ { - 1} & 7 & 0 \cr 2 & 1 & { - 3} \cr 3 & 4 & 1 \cr } } \right| = A\), then \(\left| {\matrix{ {13} & { - 11} & 5 \cr { - 7} & { - 1} & {25} \cr { - 21} & { - 3} & { - 15} \cr } } \right|\) is
A
\({A^2}\)
B
\({A^2} - A + {I_3}\)
C
\({A^2} - 3A + {I_3}\)
D
\(3{A^2} + 5A - 4{I_3}\)
Open complete paper
11
2018 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2018
If \({S_r} = \left| {\matrix{ {2r} & x & {n(n + 1)} \cr {6{r^2} - 1} & y & {{n^2}(2n + 3)} \cr {4{r^3} - 2nr} & z & {{n^3}(n + 1)} \cr } } \right|\), then the value of

\(\sum\limits_{r = 1}^n {{S_r}}\) is independent of
A
only x
B
only y
C
only n
D
x, y, z and n
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12
2018 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2018
If the following three linear equations have a non-trivial solution, then

x + 4ay + az = 0

x + 3by + bz = 0

x + 2cy + cz = 0
A
a, b, c are in AP
B
a, b, c are in GP
C
a, b, c, are in HP
D
a + b + c = 0
Open complete paper
13
2018 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2018
In a third order matrix A, aij denotes the element in the ith row and jth column. If aij = 0 for i = j

= 1 for i > j

= \(-\) 1 for i < j

Then the matrix is
A
skew symmetric
B
symmetric
C
not invertible
D
non-singular
Open complete paper
14
2018 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2018
If the polynomial \(f(x) = \left| {\matrix{ {{{(1 + x)}^a}} & {{{(2 + x)}^b}} & 1 \cr 1 & {{{(1 + x)}^a}} & {{{(2 + x)}^b}} \cr {{{(2 + x)}^b}} & 1 & {{{(1 + x)}^a}} \cr } } \right|\), then the constant term of f(x) is
A
\(2 - {3.2^b} + {2^{3b}}\)
B
\(2 + {3.2^b} + {2^{3b}}\)
C
\(2 + {3.2^b} - {2^{3b}}\)
D
\(2 - {3.2^b} - {2^{3b}}\)
Open complete paper
15
2019 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2019
Let \(A = \left[ {\matrix{ 3 & 0 & 3 \cr 0 & 3 & 0 \cr 3 & 0 & 3 \cr } } \right]\). Then, the roots of the equation det \((A - \lambda {I_3})\) = 0 (where I3 is the identity matrix of order 3) are
A
3, 0, 3
B
0, 3, 6
C
1, 0, \(-\)6
D
3, 3, 6
Open complete paper
16
2019 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2019
Let A be a square matrix of order 3 whose all entries are 1 and let I3 be the identity matrix of order 3. Then, the matrix \(A - 3{I_3}\) is
A
invertible
B
orthogonal
C
non-invertible
D
real Skew Symmetric matrix
Open complete paper
17
2019 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2019
If \(A = \left( {\matrix{ 5 & {5x} & x \cr 0 & x & {5x} \cr 0 & 0 & 5 \cr } } \right)\) and \(|A{|^2} = 25\), then | x | is equal to
A
\({1 \over 5}\)
B
5
C
52
D
1
Open complete paper
18
2019 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2019
If M is any square matrix of order 3 over R and if M' be the transpose of M, then adj(M') \(-\) (adj M)' is equal to
A
M
B
M'
C
null matrix
D
identity matrix
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19
2019 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2019
The system of equations

$$\eqalign{ & \lambda x + y + 3z = 0 \cr & 2x + \mu y - z = 0 \cr & 5x + 7y + z = 0 \cr}$$

has infinitely many solutions in R. Then,
A
\(\lambda\) = 2, \(\mu\) = 3
B
\(\lambda\) = 1, \(\mu\) = 2
C
\(\lambda\) = 1, \(\mu\) = 3
D
\(\lambda\) = 3, \(\mu\) = 1
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20
2019 · Mathematics · Algebra · Matrices And Determinants
WB JEE 2019
Let A and B be two square matrices of order 3 and AB = O3, where O3 denotes the null matrix of order 3. Then,
A
must be A = O3 , B = O3
B
if A \(\ne\) O3, must be B \(\ne\) O3
C
if A = O3, must be B \(\ne\) O3
D
may be A \(\ne\) O3, B \(\ne\) O3
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Showing 20 of 74 questions